Research

In most of the organic reactions, we get more than one product. Out of which one could be our desired product. In the current work, we are interested in studying how the product selectivity of chemical reactions can be modulated inside an optical cavity. We present classical and quantum dynamical studies on a model potential, mimicking Post-Transition State Bifurcation (PTSB) reactions, coupled to a single cavity mode.

Here in this study, we have used a linear form of the dipole function along the reaction coordinate. We have studied quantum dynamics starting with an initial  Gaussian wavepacket in the reactant well and corresponding classical dynamics with the Wigner transformed phase space density function. We have computed individual domain probability (defined in Eqn.~\ref{pd}) in two product wells, and from their time-averaged values, we have found out the branching ratio (BR=$\bar{P_{1}}/\bar{P_{2}}$) of two products.

$\bar{P_{1}}$ and $\bar{P_{2}}$ are the time-averaged domain probabilities for the deeper well and shallower well, respectively.

In Fig.2(a), we have shown the branching ratio (BR) of two products against the frequency of the cavity mode. We can make several observations here. First, we observe a significant enhancement ($\sim 25\%$) of one product ($P_{1}$) over another when the cavity mode is tuned near the Harmonic frequency of the deeper product well ($P_{1}$) compared to their off-cavity value (dotted line). Second, there is an excellent agreement between classical (blue, circle) and quantum (red, square) dynamics, as also evident from Fig.2(b), where individual domain probabilities are shown with time for a particular value of $\omega_{c}$.

Now the question is: what is the mechanism of this enhancement of selectivity? In Fig.3, we have shown different energy components with time for three different values of $\omega_{c}$. It is quite clear that, when the cavity mode is ``on-resonance" with the $P_{1}$ product well Harmonic frequency (Fig.3(b)), a significant amount of coherence energy transfer is happening between the reaction coordinate and the cavity mode. Furthermore, dwell-time distribution (Fig.4) shows that in the ``on-resonance" condition, trajectories get trapped in the product well for significantly longer times, which leads to enhancement of the branching ratio compared to the off-cavity value. Here are the key findings from this work: